This paper argues that Burley's theory of simple supposition is not as it has usually been presented. The prevailing view is that Burley and other authors agreed that simple supposition was in every case supposition for a universal, and that the disagreement over simple supposition between, say, Ockham and Burley was merely a disagreement over what a universal was (a piece of the ontology? a concept?), combined with a separate disagreement over what terms signify (the speaker's thoughts? the objects the thoughts are about?).In fact, however, Burley explicitly allows that some instances of simple supposition are for an individual, and that in certain cases personal supposition and simple supposition coincide. The present paper explores Burley's theory on this topic, and proposes a way of thinking about the metaphysics and the semantics that makes sense of what he says.